Abstract
We study some families of finite groups having inner class-preserving automorphisms. In particular, let G be a finite group and S be a semidihedral Sylow 2-subgroup. Then, in both cases when either Sym(4) is not a homomorphic image of G and \(Z(S) < Z(G)\) or G is nilpotent-by-nilpotent, we have that all the Coleman automorphisms of G are inner. As a consequence, these groups satisfy the normalizer problem.
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The author is grateful to the referee for the interest expressed in the results shown and for the valuable suggested references that improve the bibliography of the manuscript.
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Aragona, R. Coleman automorphisms of finite groups with semidihedral Sylow 2-subgroups. Acta Math. Hungar. (2024). https://doi.org/10.1007/s10474-024-01408-z
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DOI: https://doi.org/10.1007/s10474-024-01408-z
Key words and phrases
- class-preserving automorphism
- Coleman automorphism
- semidihedral 2-group
- Sylow 2-subgroup
- normalizer problem